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Summary:This paper provides comprehensive empirical evidence that supports the predictions of Sargent and Wallace's (1981) "unpleasant monetarist arithmetic" that an increase in public debt is typically inflationary in countries with large public debt. Drawing on an extensive panel dataset, we find that the relationship holds strongly in indebted developing countries, weakly in other developing countries, but generally not in developed economies. These results are robust to the inclusion of other variables, corrections for endogeneity biases, and relaxation of common-slope restrictions and are invariant over sub-sample periods. We estimate a VAR to trace out the transmission channel and find the impulse responses consistent with the predictions of a forward-looking model of inflation. Wealth effects of public debt could also affect inflation, as posited by the fiscal theory of the price level, but we do not find supportive evidence. The results suggest that the risk of a debt-inflation trap is significant in highly indebted countries, and pure money-based stabilization is unlikely to be effective over the medium term. Our findings stress the importance of institutional and structural factors in the link between fiscal policy and inflation.